聚合物共混热力学ppt课件

1、.,第二章 聚合物聚合物共混热力学,高分子合金,.,第一节 聚合物聚合物体系的相图,.,图2-1（a）：聚合物A/聚合物B 二元共混体系的相图。 (a) A blend with a UCST (upper critical solution temperature).,一、二元共混体系的相图,.,图2-1（b）：聚合物A/聚合物B 二元共混体系的相图。 (b) A blend with an LCST (lower critical solution temperature).,.,图2-1（c）（d）：聚合物A/聚合物B 二元共混体系的相图。 (c) A blend with an LCS

2、T above a UCST。 (d) A blend with a UCST above an LCST (closed phase diagram)。,.,图2-1（e）：聚合物A/聚合物B 二元共混体系的相图。(e) A blend with a tendency toward greater solubility at intermediate termperatures.,图2-2 双峰形相图（in the case of polystyrene-polybutadiene-solvent mixtures and for mixtures of styrene and isopre

3、ne oligomers.),.,The calculated phase diagram for a strictly two-component system, that is, a mixture of two monodisperse polymers, could resemble any of those in Figure 2-1 in which systems with either an upper critical solution temperature (UCST) or a lower critical solution temperature (LCST) or

4、both or a tendency toward both are shown. Real polymer blends, even though synthetic polymers are never monodisperse, exhibit phase diagrams that resemble these with some variations, with the exception of the diagram shown in Figure 2-1(d).,.,Blends that have positive (endothermic) heats and entropi

5、es of mixing usually tend to exhibit UCST, whereas blends that have negative (exothermic) heats and entropies of mixing usually exhibit LCST. In addition, two-peaked coexistence curves have been observed for certain polymer blends such as polystyrene-polybutadiene in the presence of solvent and for

6、blends of styrene and isoprene oligomers in the absence of solvent.,.,表2-1 部分共混体系的相关系研究结果。,.,If the free energy of mixing can be calculated for all possible compositions of the mixture of interest, then it becomes possible to calculate the values of temperature, pressure, and composition at which th

7、e mixture will form a stable single phase, that is, will be miscible. At the same time, it becomes possible to calculate not only the compositions at which the mixture will always separate into more than one phase (unstable compositions), but also those compositions at which the mixture may either f

8、orm a single phase if clean and relatively undisturbed or, at equilibrium, will separate into several phases (metastable compositions).,.,尽管相图是聚合物-聚合物合金体系的重要基础数据的来源，但文献中具有完整的热力学相关系资料的共混体系并不是很多。这可能有多方面的原因，例如： 实验温度限制：许多不相容体系的 LCST 或者 UCST 都不在容易进行实验的温度范围或者聚合物可能耐受的温度范围之内； 实验技术上的困难：例如，实验研究中多采用光散射法观察共混物的散

9、射光强随温度的变化来确定相界，但要求体系中组分聚合物间有较大的折光指数差别，同时分相时产生的粒子应足够大以产生较强的散射光。 聚合物本身的性质：聚合物大分子扩散速度太慢，不易建立相平衡。 因此，正确测定并得到完整的相图并不是很容易。,.,图2-3：一定温度和压力下 “聚合物A/聚合物B/溶剂S” 三元体系组成的三角形表示法。,O点组成： 20A 32B 48Solvent,二、三元体系的相图,.,图2-4： （a）聚合物A/聚合物B/溶剂S 三元体系的相图。 聚合物 A 与聚合物 B 不相容，但分别与溶剂相容。例如：PS/PP/甲苯 体系。,.,图2-4：（b）聚合物A/聚合物B/溶剂S 三元

10、体系的相图。 三组分之间两两相容，但当混合在一起时，体系在某些组成范围内会发生相分离。例如： PS/PVME/CHCl3 体系； 丁基橡胶/EPDM/苯； 无规PP/PE/二苯基醚。,Single-phase region,.,第二节 相分离的热力学和临界条件,.,一、Flory-Huggins 似晶格模型理论,假定： 高分子在溶液中的排列是一种晶格的有序排列；每个溶剂分子占一个格子，每个高分子占有 x 个格子，x 为高分子的链节数，可近似地看作高分子的聚合度（也就是说，每个高分子链节的体积与一个溶剂分子的体积相等）。,每个高分子链节占有任一格子的几率相等。 高分子链为柔性链，所有构象具有相同

11、的能量。 所有的高分子具有相同的链节数（聚合度），即为单分散的。,.,1. 高分子溶液的混合熵：,Sm 仅表示由于高分子链节在溶液中排列的方式与其在本体中排列方式的不同而引起的熵变，并未考虑在溶解过程中由于高分子与溶剂分子相互作用的变化所引起的熵变，因此又称为组合熵（combinational entropy）,N1，n1溶剂分子的个数和摩尔数； N2，n2溶液中高分子的个数和摩尔数。,.,2. 高分子溶液的混合热焓：, 称为 Flory-Huggins 相互作用参数，反映了高分子与溶剂混合时引起的相互作用能的变化，kT 的物理意义表示一个溶剂分子放到高聚物中所引起的能量变化，12 为生成一对

12、【高分子链节溶剂分子】时的能量变化。 z 为晶格的配位数，表示一个格子被一个高分子链节占领后，其周围可被第二个高分子链节或溶剂分子占领的格子数。,.,3. 高分子溶液的混合自由能：,4. 溶液中溶剂和高分子溶质的化学位变化：,.,5. 相平衡和临界条件：,.,1. 聚合物聚合物共混热力学 Scott 和 Tompa 将 Flory-Huggins 用于高分子溶液的热力学理论扩展应用于由 nA 摩尔聚合物 A 和 nB 摩尔聚合物B混合而成的聚合物/聚合物共混体系，推导出了A/B 共混体系的混合熵、混合热焓以及混合自由能，如下：,xA和A聚合物A的链节数和体积分数； xB 和B 聚合物B的链节数

13、和体积分数； AB聚合物 A、B 链段间的 Flory-Huggins 相互作用参数。,二、聚合物共混体系的相分离热力学和临界条件,.,Vr参考体积（the reference volume），定义 为每摩尔聚合物链节的体积。,.,图2-5： 一定温度下 A/B 聚合物共混体系的混合自由能随组成的变化（曲线旁的数值是相互作用参数 AB 的值，xAxB100）。,和 为相应于两个极小自由能的两个平衡相的组成。如果体系的总组成处于 和 之间，发生相分离时就会分成组成分别为 和 的两相，因为这样可使整个体系具有更小的自由能而更加稳定。,.,2. 相分离热力学和临界条件 相分离的临界条件也就是曲线中相

14、应于两个自由能极小值的两个拐点（点 K 和点 I）出现的条件，即：,.,第三节 相分离机理及双节线和旋节线,.,图2-6：A/B 聚合物共混体系的混合自由能对组成的变化及相应的旋节线（spinodal）和双节线（binodal）。 双节线；- 旋节线,旋节线（SD）机理（Spinodal Decompostion Mechanism） 成核与生长（NG）机理（Nucleation and Growth Mechanism）,一、相分离机理,.,旋节线机理的相分离过程没有热力学位垒的限制，因此分相过程通常进行得较快，得到的两相的组成是逐步变化的，会逐渐接近双节线所要求的平衡相组成。另外，由于相分

15、离能自动发生，所以体系内到处都有分相现象，故而分散相相区之间会有一定程度的相互连接、相互交叠。最后，如果时间足够长，且体系的粘度不太高，则原来在一定程度上相互连接的分散相会相互聚集成为分立的球形，分散于连续相中，以降低两相间的表面能，使体系稳定。,.,图2-7：“旋节线相分离机理”示意图。（a）组成变化；（b）相结构变化。（t 为时间，t0 t1 t2 t3。）,.,图2-8 聚合物共混体系按 SD（旋节线机理）进行相分离时的形态结构变化示意图。,.,旋节线（SD）机理 s s,成核与生长（NG）机理 b s s b,.,成核与生长机理的相分离过程无法通过体系自身组成的微小涨落而实现，而是必须

16、首先在体系中克服位垒形成分散相（其组成为平衡相组成 或 ）的“核”，“核”一旦生成，便会逐渐扩大，即所谓的“生长”。这种相分离过程通常需要较长的时间，而且，分散相相区之间一般不会相互连接，分相过程一直持续到两相的含量达到符合杠杆原理所要求的量为止。,.,图2-9： “成核与生长相分离机理”示意图。（a）组成变化；（b）相结构变化。（t 为时间，t0 t1 t2 t3。）,.,无论是“旋节线机理”还是“成核与生长机理”，如果体系最终能够达到平衡，则两种相分离的结果是没有本质差别的。然而，在实际研究中，无论是熔融共混还是溶液共混，由于聚合物共混体系的高粘度，真正的平衡是很难实现的。因此，这两种不同

17、的相分离机理就可能导致完全不同的相形态和性质。 对于旋节线机理而言，不平衡的相分离会使最后得到的两相的组成差别比平衡相的组成差别小，而且分散相之间仍会有一定程度的相互交叠，形成表观的相容；而成核与生长机理的不平衡态则表现为相分离根本没有发生，或者得到的分散相的量比平衡状态时的要少。,.,1. 旋节线,2. 双节线,二、旋节线和双节线的热力学方程,.,.,三组分体系的旋节线方程：,三、“聚合物A/聚合物B/溶剂S” 三组分体系共混热力学,.,“对称”的三组分体系的双节线方程：, 聚合物间的“有效相互作用参数”（the effective interaction parameter）,.,The

18、binodal equation of the three-component mixture in the symmetrical case did not depend on AS or BS, the presence of solvent served only to diminish the effective interaction parameter between the polymers, that is, AB(1-S) can be considered the effective interaction parameter between the polymers in

19、 this case. When there is a great deal of solvent present, that is, when S 1, the effective interaction parameter between the two polymers approaches zero, and the whole system will form a single phase.,.,“对称” 三组分体系的（近似）相分离临界条件：,The calculated approximate plait point is quite analogous to the critic

20、al point in binary polymer blends.,.,These equations allow calculation of the minimum volume fraction of solvent necessary to “compatibilize” the two polymers, or in other words, the minimum volume fraction necessary to form a single-phase solution, which depends on the degree of polymerization of e

21、ach polymer and on the interaction parameter between the two polymers.,The above equation indicate that the same minimum volume fraction of any solvent that dissolves each polymer separately will give a single phase in the three-component system. This prediction is not strictly true, but it serves a

22、s a reasonably accurate rule for most system.,.,图2-10 PS/PVME 共混体系的相图（PCM 研究结果）。空心点为旋节线机理，实心点为成核与生长机理。 （ T. Nishi, T. T. Wang, T. K. Kwei, Macromolecules, 8, 227, 1975.）,光学或电子显微镜 光散射法 DSC,相分离的实验研究,.,图2-11 PMMA/PnBMA（50/50 wt%）共混物在不同温度下退火 30min 后的扫描得到的 DSC 热谱（升温速率：10/min）。,.,图2-12 PMMA/PnBMA 共混体系的相图（

23、DSC 研究结果）。 相容；不相容 （ T. Sato, M. Endo, T. Shiomi and K. Imai, Polymer, 1996, 37, 2131.）,.,图2-13 PMMA/PC 共混体系的储存模量对温度的变化，试样 B1 和 B3 的组成 (PMMA/PC ) 分别为 82/18 和 41/59 。 （ G. Eastmond, M. Jiang, M. Malinconico, Polymer, 24, 1162, 1983.),.,表2-2：溶剂对 PS/PVME 共混体系相容性的影响 （1溶剂，2PS，3PVME， 0）,（ A. Robard, D. Pat

24、terson, G. Delmas, Macromolecules, 1977, 10, 706）,.,图2-14 PS/PVME/CHCl3 体系的旋节线（计算结果）。曲线旁的数字为温度（）。PS： ； PVME： 。 （ A. Robard, D. Patterson, G. Deln, Macromolecules, 10, 706, 1977.）,.,FloryHuggins 格子模型理论的缺陷： 忽略了体系的可压缩性（自由体积），没有考虑溶解（混合）前后体系体积的变化（V0），而体积的变化必然引起组分之间相互作用的变化，破坏混合过程的随机性，引起熵值的减小。,Prigogine-Fl

25、ory 状态方程理论,.,特征参数：,对比体积和对比温度：,二元溶液体系的状态方程,.,当温度由 0K 变化到相分离临界温度时：,因此，对于不同的相互作用类型，综合自由体积效应，体系相互作用参数 值 随温度的变化趋势将出现抛物线型和单调上升的曲线两种情况。,二元聚合物共混体系的状态方程：,.,图2-15 色散力（a）、特殊相互作用（a）和自由体积（c）对相互作用参数的贡献随温度的变化示意图。 （c）是（a）和（b）共同作用的结果，预示了混合体系 UCST 和 LCST 的存在；（d）是（a）和（b）共同作用的结果，预示了 LCST 的存在。,.,The Determination of the

26、 Thermodynamic Interaction Parameters in Polymer Blends (B. Riedl and R. E. Prudhomme, Poly. Eng Sci., 1984, 24, 1291),第四节 相互作用参数的测定,.,(T. Nishi and T. T. Wang, Macromolecules, 1975, 8, 909),Figure 2-16 DSC thermograms of the quenched PVF2/PMMA samples with different compositions at the heating rate

27、 of 10/min.,一、熔点降低法（Melting Point Depression）,.,Figure 2-17 DSC thermograms of the solution-cast PVF2/PMMA samples with different compositions at the heating rate of 10/min.,.,根据 Flory-Huggins 的似晶格模型理论，在溶液（高分子稀释剂体系）中，聚合物溶质相对于纯液体聚合物（以聚合物熔融态作为参比态）的化学位之差 2 为：,令 Vu 和 V1 分别表示高分子链重复单元（链节）和稀释剂分子的摩尔体积，则（xV1

28、/Vu）可近似表示每个高分子链所含有的重复单元数，因此，每摩尔聚合物链重复单元的化学位改变为：,.,则高分子共混物中可结晶组分（聚合物 2）的链重复单元的化学位与其在纯液体（熔体）状态下的化学位之差为：,假定在可结晶组分结晶时，非晶组分 2（稀释剂）不进入晶相，则在熔点 Tm 时，在两相平衡的条件下，除去温度和压力相等外，结晶组分的化学位在晶相和液相（熔体）两相中是相等的，即：,.,H2u，S2u可结晶组分2 每摩尔链重复单元的熔融热和熔融熵； Tm0可结晶组分2 的平衡熔点（可由外推法测得）。,因此，,.,其中： V2u, V3u两种聚合物组分的重复单元的摩尔体积； 3聚合物组分3（可结晶组

29、分）体积分数； Tm, Tm0可结晶组分3 在共混物体系中的熔点和纯态下的平衡熔点； H3可结晶组分3 完全结晶时的熔融热焓； 23基于可结晶组分3 的聚合物聚合物相互作用参数， 。,.,Table2-5 Polymer-polymer interaction parameters of several miscible polymer blends from the melting-point depression method.,*V2, the volume of one polymer molecule, not of the segment. This remark also hol

30、ds for Table 2-6 and 2-8.,.,Figure 2-18 Dependence of the interaction parameter 23 on blend composition from melting-point depression () and SAXS () for PMMA/PVF2 blends at 200. (J. H. Wendorff, J. Polym. Sci., Polym. Lett. Ed., 1980, 18, 439),.,The melting-point depression technique is a very valua

31、ble method for measuring the interaction parameter 23. It has the advantage of not involving the use of a probe nor disrupting the polymer-polymer interaction, contrary to most other methods suggested in the literature. However, it gives the interaction parameter 23 only at one temperature, which is

32、 an important limiting factor.,.,Vapor sorption is another phenomenon from which polymer-polymer interaction parameters can be calculated. This techniques has been used for some time to characterize polymer-solvent interaction. It involves measuring the amount of solvent vapor retained at equilibriu

33、m by a polymer sample.,对于由溶剂1 和聚合物2 形成的溶液体系，溶剂1 的活度为：,对于由聚合物2 和聚合物3 形成的共混体系，在有少量溶剂1 （“探针”）存在的条件下：,二、气相吸附（Vapor Sorption）,.,因此，只要测得某一特定温度下混合体系内聚合物所吸附的溶剂蒸汽量以及两种聚合物组分与溶剂间的相互作用参数，即可由上式计算出聚合物聚合物相互作用参数。,Table2-6 Polymer-polymer interaction parameters of several miscible polymer blends from the vapor sorpt

34、ion method.,.,For PS/PVME blends, the values of 23, which are composition and temperature dependent, are negative in accord with the observed miscibility of this blend. In addition, the temperature dependent of the interaction parameter enabled these authors to predict both the upper and lower cloud

35、 at various compositions.,.,Inverse-phase gas chromatography (IPGC) has often been used to investigate interaction between a probe, typically a small volatile molecule, and a liquid immobile phase like a long chain alkane. This method can be extended to investigate probe-polymer interactions, polyme

36、r-polymer interactions, as well as plastifier-polymer and plastifier-plastifier interactions.,Given an inert carrier gas, a volatile probe (1) present in small concentration as vapor, and a immobile polymer (2) liquid phase coated on an inert solid support, the interaction parameter at infinite dilu

37、tion between the vapor and the immobile phase is given by the following equation:,三、反相气相色谱法（Inverse-Phase Gas Chromatography）,.,2, V2the specific volume and molar volume of the polymer； P10 the vapor pressure of the probe in the column； Vg0，V1the specific retention volume and molar volume of the pro

38、be; B11the second virial coefficient of the probe in the vapor phase.,The above equation also enables calculation of 13:,.,The polymer-polymer interaction parameter 23 is then calculated from the following equation:,.,Table2-6 Polymer-polymer interaction parameters of several miscible polymer blends

39、 from the vapor sorption method.,( to be continued ),.,Values of 23 determined by IPGC vary slightly with the probe selected. However, this variation may not be characteristic of IPGC. Values of 23 determined by IPGC are also dependent on blend composition and temperature. The differences in polymer

40、 coating thickness and uniformity, and errors in the evaluation of column loading may result in fluctuation in 23 values. For a given blend, the obtained values by IPGC of homogeneous and phase-separated blend are different.,.,Although column preparation is time consuming in IPGC, once the value of

41、12 for different polymers are evaluated, one can rapidly proceed to blends of different compositions and obtain 23. In view of the aforementioned variations, such data are to be used with caution, but can be quite meaningful, especially for a systematic evaluation of variations of 23 between a homop

42、olymer and a homologous series of polymers.,.,Small-angle neutron scattering (SANS) permits determination of the bulk values of 23, second virial coefficients, and chain dimensions. The methods requires the deuteration of a fraction of the polymer to increase its scattering cross-section. In a blend

43、, the deuterated polymer then acts as a “solute” dispersed in a “solvent” composed of undeuterated molecules of the same kind and molecules of the second polymer.,四、中子散射（Neutron Scattering）,.,Values of 23 are obtained by constructing a Zimm plot. This method is of course reminiscent of the classical

44、 polymer-solution light-scattering technique. The above equation is the same in both cases, except for the constant K which is different.,Table2-7 Polymer-polymer interaction parameters from SANS.,* Number indicates the percent of acrylonitrile in the copolymer.,.,The SANS method is free from the pr

45、oblems encountered with probes in vapor sorption and IPGC methods, and in short, it appears to be quite promising despite the limited availability of the equipment required. It should be noted that it permits measurements at temperatures inferior to Tm and/or Tg, which are not possible with previous

46、 methods.,.,Small-angle X-ray scattering (SAXS) can also be used to determine 23. In this method, the ratio of the scattered intensity I(s) to incident intensity I0 is given by:,Iethe scattering factor of an electron; Vthe scattering volume; sthe scattering vector, s = 4sin(/2), is the scattering an

47、gle and the wavelength of the X-ray radiation; S(s)the scattering factor which is related to the chemical potential change of the components in the mixture and therefore to 23.,五、小角X光散射（Small-Angle X-Ray Scattering）,.,In general there is agreement between polymer-polymer interaction parameters measu

48、red through five different methods These methods are quite varied and each of them offers a number of advantages and disadvantages.,It should be noted that the melting-point deperssion method allows measurements of 23 only at the melting temperature Tm of the semi-crystalline component of the blend;

49、 the IPGC method allows measurements of 23 at temperatures above Tm for a crystalline blend, and above Tg for an amorphous blend, whereas the scattering technique allow measurement over a wide range of composition and temperature, above or below Tm and Tg.,.,There is some variation of the 23 paramet

50、er, as can be seen through a comparison of the different values associated with the PMMA/PVF2 blends in four of the five techniques reviewed. These variations may be due to the peculiarities of the techniques used and to the tendency of some authors to give an average 23 parameter for the whole comp

51、osition range of the blend. However, the value of 23 is composition dependent. In addition, the above comparison does not take into account variation of 23 as a function of molecular weight, which are known to occur.,.,X. Lu and R. A. Weiss, Macromolecules, 1992, 25, 3242. Y. S. Chun, H. S. Lee, H.

52、C. Jung et al., JAPS, 1999, 72, 733 Lu and Weiss derived the relationship between the Tg and the interaction parameter of miscible polymer blends. Later, Chun et al. modified the Lu and Weiss equation from the Tg as follows:,六、玻璃化转变温度法,Tgm the observed Tg of the blend; w1 and w2 the weight fraction

53、of polymer 1 with Tg1 and of polymer 2 with Tg2 respectively; Ti the width of the glass transition.,.,M1 and M2 the molecular weights of the repeating units in polymer 1 and 2 respectively; 1 and 2 the density of the component 1 and 2 respectively; Cp the specific heat increment at Tg; Cp the specific