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Mater. Chem.<\/i> <b>2009<\/b>. 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Mater. Chem. 2009. DOI: 10.1039\/b815289f\u3002 \u6b65\u884c 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W. 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x_2\\right]$$\u800cFlory--Huggins\u7406\u8bba\u7ed9\u51fa\u7684\u5c0f\u5206\u5b50\u6eb6\u5242+\u7ebf\u5f62\u9ad8\u805a\u7269\u6eb6\u8d28\u7684\u7ed3\u679c\u662f\uff1a$$\\Delta_\\text{mix}S=-R\\left[n_1\\ln\\varphi_1+n_2\\ln\\varphi_2\\right]$$\u4ee5\u4e0a\u8ba8\u8bba\u90fd\u5047\u5b9a$\\Delta_\\text{mix}H=0$\uff0c\u6216\u8005\u9650\u4e8e\u683c\u5b50\u6a21\u578b\u6765\u8bf4\u5c31\u662f\u4e0d\u540c\u6784\u5f62\u7684\u5185\u80fd\u76f8\u540c\u3002\u8fd9\u88ab\u79f0\u4e3a\u65e0\u70ed\uff08athermal\uff09\u6eb6\u6db2\uff08\u662f\u56e0\u4e3a\u7113\u5386\u53f2\u4e0a\u88ab\u79f0\u4e3a\u201cheat\u201d\uff0c\u5176\u5b9e\u8fd9\u8ddf\u70ed\u5bb9\u6216\u71b5\u4e0d\u76f4\u63a5\u76f8\u5173\uff0c\u53cd\u800c\u662f\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd\u7684\u4f53\u73b0\uff09\u3002\u5982\u679c\u6309\u7167\u60ef\u4f8b\u7528\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7406\u60f3\u6df7\u5408\u7269\u4f5c\u4e3a\u6807\u51c6\u6001\uff0c\u90a3\u4e48Flory--Huggins\u7684\u7ed3\u679c\u4f53\u73b0\u7684\u7ed3\u8bba\u5c31\u662f\uff0c\u4ec5\u56e0\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u4e5f\u4f1a\u5236\u9020\u51fa\u975e\u96f6\u7684\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\uff0c\u4e14\u8fd9\u4e2a\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\u662f\u7eaf\u71b5\u53d8\u3002 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Fowler\u63d0\u51fa\u5927\u4e00\u70b9\u7684\u5206\u5b50\u53ef\u4ee5\u8003\u8651\u5360\u4e24\u4e2a\u683c\u5b50\u3002\u4ed6\u548cG. Rushbrook\u53d1\u8868\u7684\u8fd9\u79cd\u8ba1\u7b97\u7ed3\u679c\u8bc1\u5b9e\u4e86\u8fd9\u4ef6\u4e8b\u3002\u4ec5\u4ec5\u4f5c\u51fa\u8fd9\u4e00\u5c0f\u6b65\u7684\u63a8\u5e7f\uff0c\u6570\u5b66\u63a8\u5bfc\u7684\u96be\u5ea6\u5c31\u5927\u589e\u3002\u539f\u6587\u53ea\u8ba8\u8bba\u4e86$N_1\\ll N_2$\u6216$N_1\\gg N_2$\u7684\u60c5\u51b5\u3002H. Bethe\u63d0\u51fa\u4e86\u4e00\u79cd\u65b9\u6cd5\uff0c\u73b0\u5728\u79f0\u4e3aBethe--Peierls\u8fd1\u4f3c\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u8003\u8651\u4e8c\u4f53\u76f8\u5173\u6027\u4e0b\u7684\u6784\u5f62\u6570\uff0c\u5373\u53ef\u5f97\u5230\u6982\u7387$p_{ij},\\quad i,j=A,B$\u3002\u8fd9\u4e2a\u65b9\u6cd5\u8fc5\u901f\u88ab\u5f20\u5b97\u71e7\u548cA. Miller\u7b49\u7528\u4e8e\u8003\u8651\u5927\u5206\u5b50\u6eb6\u8d28\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4ece\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u4e00\u76f4\u63a8\u5e7f\u5230\u4e00\u822c\u7684$r$\u805a\u4f53\u3002\u8fd9\u4e24\u4e2a\u4eba\u9760Bethe\u65b9\u6cd5\u5199\u4e0b\u6784\u5f62\u6570\uff0c\u5f97\u5230\u65e0\u70ed\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u53d8\u90e8\u5206\u3002W. Orr\u8fdb\u4e00\u6b65\u628aBethe\u8fd1\u4f3c\u4e0b\u7684\u6df7\u5408\u7113\u4e5f\u5199\u51fa\u6765\u4e86\u3002E. Guggenheim\u7528\u53e6\u4e00\u79cd\u66f4\u4f18\u96c5\u7684\u65b9\u6cd5\uff0c\u5f97\u51fa\u4e86\u8ddf\u7528Bethe\u65b9\u6cd5\u4e00\u6837\u7684\u7ed3\u679c\uff0c\u5e76\u8bc1\u660e\u4e24\u79cd\u65b9\u6cd5\u662f\u7b49\u4ef7\u7684\u3002\u8fd9\u4e9b\u6765\u81ea\u82f1\u56fd\uff08\u548c\u6211\u56fd\u5f20\u5b97\u71e7\u5728\u82f1\u56fd\u7559\u5b66\u65f6\uff09\u7684\u8d21\u732e\uff0c\u57fa\u672c\u7cfb\u7edf\u6027\u5730\u7ec8\u7ed3\u4e86\u805a\u5408\u7269\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7406\u8bba\u5de5\u4f5c\u3002\u53ef\u4ee5\u53c2\u8003A. Miller\u548cE. Guggenheim\u7684\u4e24\u672c\u4e66\uff1a A. Miller (1948), The Theory of Solutions of High Polymers, Clarendon E. Guggenheim (1952), Mixtures, Clarendon\u4e5f\u53ef\u4ee5\u53c2\u8003H. Tompa\u7684\u4e66\uff1a H. Tompa (1956), Polymer Solutions, Butterworths \u8fd9\u4e2aH. Tompa\u4e5f\u662f\u503c\u5f97\u4e00\u8bf4\u7684\uff0c\u4f46\u6211\u53ef\u80fd\u8981\u5c06\u5728\u53e6\u4e00\u7bc7\u6587\u7ae0\u91cc\u8bb2\u3002 \u6211\u4eec\u4eca\u5929\u6240\u719f\u77e5\u7684Flory--Huggins\u5c5e\u4e8e\u540c\u65f6\u671f\u7f8e\u56fd\u4eba\u7684\u5de5\u4f5c\u3002\u6211\u4e4b\u524d\u7684\u6587\u7ae0\u63d0\u5230\uff0c\u662fM. Huggins\u7a0d\u5fae\u6bd4P. Flory\u65e9\u51e0\u4e2a\u6708\u5f00\u59cb\u63a8\u5bfc\u9ad8\u5206\u5b50\u6eb6\u6db2\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4f3c\u4e4e\u8fd9\u79cd\u540c\u65f6\u6027\u662f\u5de7\u5408\uff0c\u4f46\u5176\u5b9eFlory\u8fd9\u4e2a\u505a\u6cd5\u662f\u53d7\u5fb7\u56fd\u5316\u5b66\u5bb6K. Meyer\u7684\u5efa\u8bae\u505a\u7684\u3002K. Meyer\u548cH. Mark\u5408\u8457\u4e86\u4e16\u754c\u4e0a\u7b2c\u4e00\u672c\u9ad8\u5206\u5b50\u79d1\u5b66\u7684\u6559\u79d1\u4e66\u3002 \u503c\u5f97\u5f3a\u8c03\u7684\u662f\uff0c\u4eca\u5929\u7684Flory--Huggins\u5f62\u5f0f\uff0c\u662fGuggenheim\u4e00\u822c\u5f62\u5f0f\u4e2d\u914d\u4f4d\u6570$z\\to\\infty$\u7684\u7279\u6b8a\u7ed3\u679c\uff0c\u6240\u4ee5\u8868\u8fbe\u5f0f\u4e2d\u4e0d\u663e\u542b$z$\uff08\u4ea4\u6362\u71b5\u53d8\u90e8\u5206\u4e0d\u542b$z$\uff0c\u7113\u53d8\u5bf9$z$\u7684\u4f9d\u8d56\u6027\u5305\u5728\u201c\u76f8\u4e92\u4f5c\u7528\u53c2\u6570\u201d $\\chi$ \u7684\u5b9a\u4e49\u4e2d\u4e86\uff09\u3002\u54ea\u6015\u662f\u9650\u4e8e\u5bfc\u51faFlory--Huggins\u7684\u4ea4\u6362\u71b5\u5f62\u5f0f\uff0c\u4e5f\u6709\u4e0d\u540c\u7684\u6570\u683c\u5b50\u65b9\u6cd5\u3002\u4eca\u5929\u8bb8\u591a\u4e2d\u6587\u9ad8\u5206\u5b50\u7269\u7406\u6559\u79d1\u4e66\u4e0a\u7684\u6570\u6cd5\uff0c\u5c31\u8ddfFlory\u5728\u81ea\u5df1\u7684\u4e66\u4e2d\u7684\u6570\u6cd5\u6709\u70b9\u4e0d\u540c\uff0c\u4f46\u90fd\u7528\u4e0d\u540c\u7684\u8fd1\u4f3c\u4e3b\u5f20\u51d1\u51fa\u4e86\u76f8\u540c\u7684\u6700\u540e\u7ed3\u679c\u3002\u5176\u4e2d\u4e00\u79cd\u5199\u6cd5\u9700\u8981\u8bf4\u201c\u5047\u5b9a\u2026","rel":"","context":"In &quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":4479,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4479","url_meta":{"origin":32,"position":3},"title":"IWEAYR-7\u603b\u7ed3(1)","author":"Andrew","date":"2012\u5e742\u670813\u65e5","format":false,"excerpt":"\u6211\u5728\u7b2c7\u5c4a\u9752\u5e74\u6d41\u53d8\u5b66\u5bb6\u7814\u8ba8\u4f1a\u505a\u7684\u4e00\u4e9b\u8bb0\u5f55\uff0c\u9646\u7eed\u505a\u4e00\u4e9b\u603b\u7ed3\u3002\u7531\u4e8e\u65f6\u95f4\u6709\u9650\u6211\u5199\u6211\u81ea\u5df1\u624d\u770b\u5f97\u61c2\u7684\u4e1c\u897f\uff0c\u4e0d\u591a\u505a\u89e3\u91ca\u3002\u4f1a\u8bae\u7684\u62a5\u544a\u8868\u73b0\u51fa\u51e0\u4e2a\u6bd4\u8f83\u96c6\u4e2d\u7684\u8bdd\u9898\u3002\u6709\u4e9b\u8bdd\u9898\u6211\u4e0d\u592a\u719f\u6089\uff0c\u5e78\u4e8f\u5bfc\u5e08\u4e00\u76f4\u5750\u6211\u65c1\u8fb9\u3002\u4efb\u4f55\u4e0d\u61c2\u7684\u4e1c\u897f\u90fd\u53ef\u4ee5\u9a6c\u4e0a\u95ee\u4ed6\u3002\u6709\u65f6\u5bfc\u5e08\u4f1a\u53eb\u6211\u76f4\u63a5\u5411\u6f14\u8bb2\u4eba\u63d0\u95ee\u3002 \u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u83b7\u53d6 \u4e3b\u8981\u662fK. Cho\u7ec4\u7684\u5de5\u4f5c \u7ebf\u6027\u7c98\u5f39\u6027\u7406\u8bba\u4ecd\u7136\u662f\u91cd\u8981\u7684\u6d41\u53d8\u5b66\u624b\u6bb5\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u9ad8\u5206\u5b50\u4f53\u7cfb\uff0c\u5305\u62ec\u7194\u4f53\u548c\u6eb6\u6db2\u3002\u8fd9\u4e9b\u4f53\u7cfb\u901a\u8fc7\u65f6\u6e29\u53e0\u52a0\uff08TTS\uff09\uff0c\u53ef\u83b7\u5f97\u201c\u5b8c\u6574\u201d\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\uff0c\u7136\u540e\u518d\u901a\u8fc7\u677e\u5f1b\u65f6\u95f4\u8c31\u4e2d\u663e\u793a\u51fa\u6765\u7684\u5feb\u6162\u6a21\u5f0f\u6765\u83b7\u53d6\u5206\u5b50\u8fd0\u52a8\u7684\u4fe1\u606f\u3002\u4eceG'\u3001G'' vs \u03c9\u66f2\u7ebf\u83b7\u5f97\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u7684\u8fc7\u7a0b\u662f\u9700\u8981\u975e\u7ebf\u6027\u62df\u5408\u3002AR-G2\u5e26\u7684Rheology Advantage\u8f6f\u4ef6\u5c31\u6709\u6b64\u529f\u80fd\u3002\u4f46\u662f\u5927\u5bb6\u8fd8\u662f\u4e00\u76f4\u63d0\u51fa\u5404\u79cd\u7b97\u6cd5\u6765\u505a\u8fd9\u4ef6\u4e8b\u60c5\uff0c\u5c31\u662f\u56e0\u4e3a\u5728\u6570\u5b66\u4e0a\u4ece\u52a8\u6001\u6a21\u91cf\u83b7\u5f97\u8fde\u7eed\u677e\u5f1b\u65f6\u95f4\u8c31H(\u03c4)\u9700\u8981\u89e3\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u90a3\u4e2aVoltera\u79ef\u5206\u65b9\u7a0b\u3002\u89e3\u8fd9\u4e2a\u65b9\u7a0b\u662f\u4e0d\u9002\u5b9a\uff08ill-posed\uff09\u7684\u53cd\u95ee\u9898\u3002\u6b63\u5219\u5316\uff08regularization\uff09\u662f\u4e00\u4e2a\u6bd4\u8f83\u5e38\u89c4\u7684\u89e3\u51b3\u65b9\u6cd5\u3002\u57fa\u4e8e\u6b63\u5219\u5316\u7684\u65b9\u6cd5\u6709\u5f88\u591a\u62a5\u9053\u3002K. Cho\u7b49\u63d0\u51fa\u65b0\u7684\u7b97\u6cd5\u4e0d\u9700\u8981\u4f7f\u7528regularization\u3002\u5728\u4f7f\u7528K-BKZ\u672c\u6784\u65b9\u7a0b\u65f6\uff0c\u8bb0\u5fc6\u51fd\u6570\u5f80\u5f80\u901a\u8fc7\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u5b9e\u9a8c\u6765\u786e\u5b9a\u3002\u901a\u8fc7TTS\u5f97\u5230\u4e86G'\u3001G''\u4e3b\u66f2\u66f2\u7ebf\u4e4b\u540e\uff0c\u662f\u8981\u7528\u4e00\u4e2a\u6709\u9650\u6a21\u5f0f\u6570\u7684Maxwell\u65b9\u7a0b\u53bb\u62df\u5408\uff0c\u5f97\u5230\u4e00\u4e2a\u79bb\u6563\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\uff0c\u624d\u80fd\u628a\u8bb0\u4e59\u51fd\u6570G(t)\u5199\u6210\u4e00\u4e2a\u6c42\u548c\u5f0f\u3002\u4e4b\u6240\u4ee5\u8981\u7528\u79bb\u6563\u8c31\uff0c\u662f\u56e0\u4e3a\u5404\u79cd\u9ad8\u5206\u5b50\u4f53\u7cfb\u7684\u8fde\u7eed\u65f6\u95f4\u8c31\u5f80\u5f80\u4e0d\u662f\u4e00\u4e2a\u7279\u5b9a\u7684\u51fd\u6570\uff0c\u53ea\u80fd\u8fd1\u4f3c\u5199\u6210\u4e00\u4e2atruncated\u7684\u7ea7\u6570\u3002K. 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